A151290 Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0) and consisting of n steps taken from {(-1, 0), (0, -1), (0, 1), (1, 1)}.

1, 2, 7, 23, 82, 297, 1092, 4074, 15316, 57993, 220913, 845017, 3245513, 12504416, 48308973, 187089688, 726028123, 2822654120, 10991682069, 42864045010, 167373921420, 654315764945, 2560630856073, 10030570526492, 39326590305594, 154311641356522, 605946719764108, 2381052954112297

Offset

0,2

Links

Table of n, a(n) for n=0..27.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0 || Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[-1 + i, -1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[i, 1 + j, -1 + n] + aux[1 + i, j, -1 + n]]; Table[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A143629 A176287 A119371 * A346627 A047002 A127497

Adjacent sequences: A151287 A151288 A151289 * A151291 A151292 A151293

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved